For the Lagrangian of fermion masses, how do I understand?

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    Fermion Lagrangian
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SUMMARY

The discussion focuses on understanding the Lagrangian formulation of fermion masses, specifically in the context of SU(2) gauge theory. The user expresses confusion regarding the expansion of the Lagrangian into components of left-handed lepton doublets (L) and right-handed lepton singlets (R). The inquiry centers on how specific matrix terms can be classified as gauge singlets within this framework. Clarification on these concepts is essential for grasping the underlying mechanics of fermion mass generation.

PREREQUISITES
  • Understanding of Lagrangian mechanics in quantum field theory
  • Familiarity with SU(2) gauge theory and its representations
  • Knowledge of fermion mass generation mechanisms
  • Proficiency in matrix notation and tensor products
NEXT STEPS
  • Study the derivation of the Higgs mechanism in the Standard Model
  • Learn about gauge invariance and its implications for particle physics
  • Explore the role of vacuum expectation values in mass generation
  • Investigate the mathematical formalism of tensor products in quantum field theory
USEFUL FOR

This discussion is beneficial for theoretical physicists, graduate students in particle physics, and anyone interested in the mathematical foundations of fermion mass generation in the context of gauge theories.

lhcQFT
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Hello, everyone.

I have a one question which is related to the fermion masses.
If you see my latex mathematics, you can know what I want to say.
Here, L means SU(2) left-handed lepton doublets and R means SU(2) right-handed lepton singlets.

So I am too much confusing to understand this mechanism. When I expanded lagrangian into components of lepton doublets and that of lepton singlets, I can't understand how these terms( (1x1) (2x2) (1x1) <= I expressed each term by using matrix notation ) can be gauge singlets? If you give me detailed explanation, I really thanks to you.

Have a good day.
 
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what latex?
 

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